Verify correspondence between Chriss–Ginzburg standard modules and p-adic standard representations

Demonstrate that the “standard modules” constructed in Chriss–Ginzburg’s Iwahori–Hecke algebra framework correspond precisely to the standard representations of p-adic groups as defined via Langlands classification, thereby validating the p-adic Kazhdan–Lusztig hypothesis in this sense.

Background

Chriss–Ginzburg established results toward the p-adic KLH using modules for the Iwahori–Hecke algebra, but the identification of their “standard modules” with p-adic standard representations requires a careful translation. The authors highlight that this verification is not yet present in the literature.

Confirming this correspondence is essential for transporting geometric multiplicity formulas from Hecke algebra modules to representations of p-adic groups, solidifying the link between perverse sheaves on parameter varieties and the Langlands classification.